The experimental estimation of frequency response functions characterizing SISO linear systems is a well established topic. Several estimators are defined in the literature, each estimator being optimal depending upon the assumptions with respect to the balance of noise between the input and output of the system. H 1 and H 2 have to be used in case of presence of noise on output and input, respectively. The H V or H s estimator is chosen if input and output are assumed to have equivalent SNR. These estimators are also established for MIMO linear systems, with additional difficulties due to the necessity of inversing cross spectral matrices. A transmissibility function is generally defined as a linear relationship between two outputs of a linear system. For SIMO systems, transmissibility functions are uniquely defined. The H s estimator is thus advised if both outputs are of equivalent SNR. In the case of MIMO systems, transmissibility functions are no more defined by the system only, it also depends on the input quantities. It is however possible to define a transmissibility matrix between two sets of outputs that is, under some assumptions, uniquely defined. This approach is especially the base of Operational Transfer Path analysis, an engineering method benefiting of a strong research effort in the last few years. This paper deals with the use of the application of MIMO system estimators to the experimental assessment of transmissibility matrices. Transmissibility matrices are generally estimated using a H 1 like approach in the literature. The possibility of using H 2 and H s is presented in this work, from the theoretical point of view and with numerical and practical illustrations.
In the challenge of reducing the weight of the vehicle structures, a particular focus has to be done on the interior noise. Indeed, the weight reduction of the structure often implies an increase of the noise in the cabin. To maintain a constant acoustic performance, acoustic packages often have to be added, the challenge being that the weight of the acoustic materials added remains lower than the weight saved in the structure. In today's engineering world, numerical simulation is the primary tool to assess the vibro-acoustic behavior of the vehicle during the design phase. To tackle the challenge of weight reduction, it is necessary to simulate accurately the vibro-acoustic response of the structure including the acoustic treatments. This paper presents the validation of a simulation method for the vibro-acoustic response of a truck cabin, taking into account the effect of acoustic treatments, in the frequency range [0-200Hz]. The method combined a modal scheme for the structure and the cavity with a physical scheme for the acoustic treatment (porous materials). The model consists in a truck cabin with its cavity and five acoustic treatments (three floormats, the headliner and the rear trim panel). A measurement campaign is performed to get reference NTFs, VTFs and local inertances. The model without any treatments is first correlated. The noise reduction given by each treatment alone as well as grouped together is simulated. The comparisons between the simulated and measured results show good agreement both in term of spectrum and amplitude. Although some discrepancies in the low frequency range remain unexplained, the method is considered as validated.
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